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Projection of the Khokhlov-Zabolotskaya Equation on the Axis of Wave Beam As a Model of Nonlinear Diffraction
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- Vasiljeva, O. A. (author)
- Moscow State Univ., RUS
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- Lapshin, E. A. (author)
- Moscow MV Lomonosov State Univ., RUS
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- Rudenko, Oleg (author)
- Blekinge Tekniska Högskola,Institutionen för maskinteknik
- Moscow State Univ, RUS Moscow MV Lomonosov State Univ., RUS (creator_code:org_t)
- MAIK NAUKA/INTERPERIODICA/SPRINGER, 2017
- 2017
- English.
- In: Doklady. Mathematics. - : MAIK NAUKA/INTERPERIODICA/SPRINGER. - 1064-5624 .- 1531-8362. ; 96:3, s. 646-649
- Journal article (peer-reviewed)
Abstract
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- An equation is obtained that describes the nonlinear diffraction of a focused wave in a half-space starting from the wave source, then through the focus region up to the far zone, where the wave becomes spherically divergent. In contrast to the Khokhlov-Zabolotskaya equation (KZ), which contains two spatial variables, the calculation of the field on the beam axis is reduced to a simpler one-dimensional problem. Integral relations that are useful for numerical calculation are indicated. The profiles of a periodic wave harmonic at the input to the medium are constructed. A comparison with the results of a numerical solution of problems based on KZ is made, which revealed a good accuracy of the approximate model. The passage of a wave through the focus region, accompanied by the formation of shock fronts, diffraction phase shifts and asymmetric distortion of regions of different polarity, is traced.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (subject category)
- art (subject category)
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- NATURAL SCIENCES
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